So you are in the Gondorian army and you just witnessed an orc or troll kill some of your comrades in battle. The orc or troll is now seriously injured and laying on the ground. The wounds are not terminal, but It cannot move. What do you do? Finish off the now helpless enemy or leave it there and hope it does not get better and later kill more of your comrades in battle? I feel a soldier in any army would finish off that enemy.
Now, a civilian who is new to the adventuring life, I could see having serious issues with it. But if he or she had just witnessed a friend or family member killed by that now helpless orc, as a LM, I think it would be perfectly fine that the character, in the moment of anger and loss, finished off that enemy. And I would not force a Shadow point on them, though if they wanted to take one for roleplaying purposes, I would accept that.
Now, back to the original question about goblin slaves, but like a previous poster said, lesser of two evils and all. Personally, my character would have more distress and worry wondering how many potential lives could be lost by letting the slaves live and leave, than by executing them for their potential past crimes against the Free Peoples. This would also be influenced by my character's race, as others have said. A dwarf would never let them leave alive. A hobbit would never take one of their lives or watch it happen, but would probably give in after arguing and let it happen. And elves and humans would be somewhere in between those two extremes, influenced by their personal history with goblins, orcs, etc.
Finally, this is not at you or most other posters here, but sometimes I think people get the Shadow of Middle-Earth and the Dark Side of the Force from Star Wars a bit muddled together. They do work similarly in some ways, and while I have never heard about Lucas being influenced by Tolkien, I have always wondered. The dangers of anger and hate are there in both systems, but I feel the penalty of having to do the lesser of two evils is punished less by Tolkien than Lucas.